Okay. Love the no help, now he thinks I'm stupid.

My friend Nick is quizzing my on stuff I don't know.
like this
Given: A= 10km S30degreesW and B= 15km S40degreesW Find the resulting vector (magnitude and direction) of the combined vectors

Please just help.
He's 19 and I'm 14.
Don't believe me? Then oh well...

Tell him you're not stupid, just ignorant of trigonometry.

24.91 @ S36°W

Hey there! Don't worry, I'm here to help you out. Understanding vectors can be tricky, but I'll do my best to explain it to you step by step.

First, let's understand the given information. We have two vectors: A and B. Vector A is 10 km in length, and it is directed 30 degrees West of South. Vector B is 15 km in length, and it is directed 40 degrees West of South.

To find the resulting vector of the combined vectors, we need to add the magnitudes of the vectors and find the direction of the resultant vector. Here's how you can do it:

Step 1: Break down vector A into its components.
To do this, we need to understand the given direction. "S30degreesW" means you start facing South and then turn 30 degrees towards the West. So, the horizontal component of vector A is A_horizontal = A * cos(30°), and the vertical component is A_vertical = A * sin(30°).

Step 2: Break down vector B into its components.
Similar to vector A, we need to break down vector B into horizontal and vertical components. "S40degreesW" means you start facing South and then turn 40 degrees towards the West. So, the horizontal component of vector B is B_horizontal = B * cos(40°), and the vertical component is B_vertical = B * sin(40°).

Step 3: Add the horizontal and vertical components separately.
Add the horizontal components of vector A and vector B, and the same with the vertical components. The horizontal component of the resultant vector is R_horizontal = A_horizontal + B_horizontal, and the vertical component is R_vertical = A_vertical + B_vertical.

Step 4: Find the magnitude of the resultant vector.
The magnitude of the resultant vector can be found using the Pythagorean theorem, which states that the magnitude (R) squared is equal to the sum of the squares of the horizontal (R_horizontal) and vertical (R_vertical) components of the vector. So, R = √(R_horizontal^2 + R_vertical^2).

Step 5: Find the direction of the resultant vector.
To find the direction, we need to determine the angle that the resultant vector makes with the South direction. You can use trigonometry to calculate this angle. The angle (θ) can be found using the formula θ = tan^(-1)(R_vertical / R_horizontal).

So, by following these steps, you can find both the magnitude and direction of the resulting vector.